QNMs of branes, BHs and fuzzballs from Quantum SW geometries

TL;DR

This paper explores the connection between quasinormal modes of various black hole and brane backgrounds and quantum Seiberg-Witten geometries, revealing how quantum effects quantize the QNM spectrum and extending the gauge/gravity correspondence.

Contribution

It extends the gauge/gravity dictionary to include a broad class of backgrounds and demonstrates how quantum SW geometries determine QNM spectra through exact methods.

Findings

Photon-spheres relate to degenerations in classical elliptic SW geometry.

Quantum effects resolve singularities and produce quantized QNM spectra.

Excellent agreement between WKB, geodetic, and numerical methods for QNM calculations.

Abstract

QNMs govern the linear response to perturbations of BHs, D-branes and fuzzballs and the gravitational wave signals in the ring-down phase of binary mergers. A remarkable connection between QNMs of neutral BHs in 4d and quantum SW geometries describing the dynamics of ${\cal N}=2$ SYM theories has been recently put forward. We extend the gauge/gravity dictionary to a large class of gravity backgrounds including charged and rotating BHs of Einstein-Maxwell theory in $d=4,5$ dimensions, D3-branes, D1D5 `circular' fuzzballs and smooth horizonless geometries; all related to ${\cal N}=2$ SYM with a single $SU(2)$ gauge group and fundamental matter. We find that photon-spheres, a common feature of all examples, are associated to degenerations of the classical elliptic SW geometry whereby a cycle pinches to zero size. Quantum effects resolve the singular geometry and lead to a spectrum of quantized energies, labeled by the overtone number $n$. We compute the spectrum of QNMs using exact WKB quantization, geodetic motion and numerical simulations and show excellent agreement between the three methods. We explicitly illustrate our findings for the case D3-brane QNMs.